Anneal-free ultra-low loss silicon nitride integrated photonics

Heterogeneous and monolithic integration of the versatile low-loss silicon nitride platform with low-temperature materials such as silicon electronics and photonics, III–V compound semiconductors, lithium niobate, organics, and glasses has been inhibited by the need for high-temperature annealing as well as the need for different process flows for thin and thick waveguides. New techniques are needed to maintain the state-of-the-art losses, nonlinear properties, and CMOS-compatible processes while enabling this next generation of 3D silicon nitride integration. We report a significant advance in silicon nitride integrated photonics, demonstrating the lowest losses to date for an anneal-free process at a maximum temperature 250 °C, with the same deuterated silane based fabrication flow, for nitride and oxide, for an order of magnitude range in nitride thickness without requiring stress mitigation or polishing. We report record low anneal-free losses for both nitride core and oxide cladding, enabling 1.77 dB m-1 loss and 14.9 million Q for 80 nm nitride core waveguides, more than half an order magnitude lower loss than previously reported sub 300 °C process. For 800 nm-thick nitride, we achieve as good as 8.66 dB m−1 loss and 4.03 million Q, the highest reported Q for a low temperature processed resonator with equivalent device area, with a median of loss and Q of 13.9 dB m−1 and 2.59 million each respectively. We demonstrate laser stabilization with over 4 orders of magnitude frequency noise reduction using a thin nitride reference cavity, and using a thick nitride micro-resonator we demonstrate OPO, over two octave supercontinuum generation, and four-wave mixing and parametric gain with the lowest reported optical parametric oscillation threshold per unit resonator length. These results represent a significant step towards a uniform ultra-low loss silicon nitride homogeneous and heterogeneous platform for both thin and thick waveguides capable of linear and nonlinear photonic circuits and integration with low-temperature materials and processes.


INTRODUCTION
Ultra-low loss silicon nitride photonic integrated circuits 1 (PICs) have the potential to reduce the size, weight, and cost, and improve the reliability of a wide range of applications spanning the visible to infrared, including quantum computing and sensing [2][3][4][5] , atomic clocks 6,7 , atomic navigation 8 , metrology 9 , and fiber optic communications 10 as well as enabling new portable applications 11 .In addition to replacing costly systems such as lasers and optical frequency combs that are relegated to bulky table-top systems, there is the potential to improve the performance for precision sciences, such as reducing laser frequency noise which is important for the manipulation and interrogation of atom, ions, and qubits 12,13 .The silicon nitride integration platform has enabled a wide range of waveguide and device designs, from thin nitride waveguides that support ultra-low loss dilute optical modes to thick nitride waveguides that are strongly confining and enhance optical nonlinearities.By varying waveguide parameters, such as nitride core thickness and width, it is possible to design characteristics such as loss, dispersion, nonlinearity, and device footprint [14][15][16] .Leveraging the properties of both thin weakly confining and thick strongly confining waveguides, this platform enables the designer to realize a wide range of components and functions including ultra-low linewidth lasers [17][18][19][20][21] , optical frequency combs 22 , optical modulators 23,24 , tunable lasers and filters 25,26 , and atom and ion beam emitters 2,[27][28][29] .
Yet, a major transformation in silicon nitride photonics is needed, where the ultra-low loss and wafer-scale CMOS foundry compatible processes of thin nitride structures and nonlinear properties of thick waveguide structures are maintained while adding the heterogeneous functionality of optical gain, high-speed modulation, electronics, and engineered thermal properties, and at the same time providing a uniform anneal-free waveguide fabrication process for both thin and thick structures.Heterogeneous and monolithic integration of thin and thick nitride photonics with materials that cannot withstand high annealing temperatures is inhibited by incompatibility with the high temperature nitride growth and high-temperature post-oxide cladding annealing process used to achieve today's low losses.Heterogeneous and monolithic integration material platforms of interest include silicon photonic circuits 30 , GaAs and InP semiconductor circuits 31,32 , and nonlinear materials such as lithium niobate 33 and tantalum pentoxide (tantala) 34 as well as materials for thermal engineering such as quartz substrates 35 .For example, efforts to limit the process temperature to under 400 °C can prevent crystallization in nonlinear tantala waveguides 34 , enable processing waveguides directly on silicon electronics, silicon photonic circuits 30,36 , thin film lithium niobate 33 , and III-V semiconductors 31,32,37 .Further limiting processing temperatures to 250 °C enables a much broader class of heterogeneous and monolithic cointegration with organic electronics 38 , polymers like polyimide (Kapton) 39 , prepackaged electronics 40 , and substrates that are damaged under thermal stress like quartz 35,41 .
Therefore, heterogeneous and monolithic integration requires a uniform anneal-free silicon nitride fabrication process that can produce a wide range of nitride core thickness waveguides, of over an order of magnitude range, while maintaining the loss and other planar and high-performance platform properties without additional process complexities such as stress mitigation and chemical mechanical polishing (CMP).State of the art thin (< 100 nm) waveguide silicon nitride photonics are essential to achieve the lowest losses that today reach 0.034 dB/m in the infrared 42,43 and sub-dB/m losses in the visible 44 .These dilute mode ultra-low loss thin waveguides are required for precision applications such as laser frequency stabilization and noise reduction, for example integrated waveguide reference cavities yielding 36 Hz integral linewidth 45 and stimulated Brillouin lasers (SBLs) 21 with sub-100 mHz fundamental linewidth 21 .This level of performance is achieved by reducing overlap of the optical mode with the etched nitride sidewalls and employing Low Pressure Chemical Vapor deposited (LPCVD) silicon nitride waveguides patterned on top of a thermal silicon dioxide lower cladding and a Tetraethyl orthosilicate -plasma enhanced chemical vapor deposited (TEOS-PECVD) upper cladding 42,43 .Yet, these processes require nitride growth temperatures as high as 850 °C 46 and annealing temperatures of 1150 °C 1,42,47 .Recent efforts to reduce the process temperatures of these dilute waveguides employed an unannealed deuterated upper cladding oxide, however, still required 1050 °C annealing of the LPCVD nitride core in order to yield losses of 1 dB/m 48 .
For high optical confinement thick nitride devices, the mainstay of nonlinear optical photonics, losses are determined primarily by sidewall scattering and nitride absorption.Thick core nitride waveguide designs utilize strong confinement to achieve efficient optical nonlinearities 15,[49][50][51] , achieving losses as low as 0.4 dB/m and resonator Q as high as 67 million 52 , requiring anneal temperatures of 1050 °C and structures for stress mitigation as well as CMP.Research to reduce the processing temperature of thick nitride waveguides has focused on deuterated silicon nitride to lower losses in the nitride core only and has not addressed lowering the deuterated oxide cladding losses [53][54][55][56][57][58] .
Therefore, these processes are not capable of realizing ultra-low loss and high resonator Q thin core (< 100 nm) waveguides and devices.Examples of low temperature thick nitride waveguides include 270°C deuterated nitride with losses down to 22 dB/m and quality factors of 1.6 million for partially etched 920 nm thick waveguides 55,59 .More recently, 270 °C deuterated nitride yielded 6 dB/m loss and 5.3 million intrinsic Q in 850 nm thick waveguides for 480 μm radius resonators and 11.9 dB/m loss and 2.9 million intrinsic Q for 150 μm radius resonators (see Supplementary Section S6) 57 , and thick waveguide deuterated Si-rich nitride waveguides demonstrated losses of 150 dB/m and resonator intrinsic Q of 1.32 x 10 5 with a 350 °C process 53,54,60 .Hydrogen-free low temperature sputtering has also been employed, combined with 300 °C deposited upper cladding, to achieve 32 dB/m losses and 1.1 million intrinsic Q in 750 nm core waveguides 61 .After 400 °C annealing these achieved 5.4 dB/m loss and 6.2 million intrinsic Q.These low temperature processes were used to demonstrate efficient optical nonlinearities including Kerr microcombs 55,56 , octave spanning supercontinuum generation 55 , and nonlinear frequency generation with Optical Parametric Oscillation (OPO) thresholds of 13.5 mW 56 and OPO threshold per unit resonator lengths down to 23.6 mW/mm 57 .To date, there has not been a demonstration of anneal-free silicon nitride waveguide fabrication, that lowers loss for both the nitride core and oxide cladding, to enable an order of magnitude range of ultra-low loss thin and thick waveguides, with maximum temperature of 250 °C for flexible heterogeneous and monolithic integration.
In this work we report a significant advance in silicon nitride integrated photonics, achieving the lowest loss to date for an anneal-free silicon nitride waveguide.Additionally, using a maximum oxide and nitride temperature of 250 °C we demonstrate the dual use capability for ultra-low loss linear and nonlinear waveguides, using the exact same fabrication process for waveguides with an order of magnitude variation in thickness (80 nm to 800 nm) without any modification in the process flow and without requiring stress mitigation or CMP.We confirm the shifted absorption peaks of our 250 °C grown deuterated Si3N4 by using Fourier transform infrared (FTIR) spectroscopy (Supplementary Section S2).The 250 °C maximum temperature is compatible with a wide range of materials including organics 38,39 .We report 1.77 dB/m loss and a ~15 million intrinsic Q for thin 80 nm core, over half an order of magnitude lower loss than previous low temperature nitride processes 57,62 .For thick 800 nm waveguides we report comparable to record-low 8.66 dB/m loss and 4.03 million intrinsic Q which is 39 % higher than low temperature deposited thick nitride devices with similar area, as well as resonators that are 7.5 times smaller in area than equivalent record-high Q low temperature fabricated device 57 .To demonstrate the quality of our anneal-free fabrication process, we report record performance linear and nonlinear applications for both ultra-low loss thin and thick nitride waveguides.For thin waveguides we demonstrate a ring resonator optical reference cavity that reduces laser frequency noise by over 4-orders of magnitude using a Pound-Drever-Hall (PDH) lock.We measure 20 Hz 2 /Hz at a 10 kHz frequency offset from carrier and reduction in the integral linewidth to under 1 kHz, a factor of over 20 times reduction over the free running linewidth.This is the first demonstration of laser stabilization using an anneal-free, low temperature waveguide reference cavity, to the best of our knowledge.This performance is only possible by realizing low loss and high Q, for a 5.36 cm long cavity, almost 20X longer than the longest low temperature processed waveguide reported to date 57 , making for a thermorefractive noise (TRN) floor 45 that was 10 3 times less than that of a typical thick nitride resonator because of the larger modal area of thin waveguides.We also confirm the quality of our 800 nm thick nitride waveguides and resonators with demonstrations of: 1) Resonant optical parametric oscillation (OPO) and Kerr-comb formation and 2) non-resonant supercontinuum generation.Anomalous dispersion is measured, with over 2 octave supercontinuum generation from 650 nm to 2.7 μm as well as four-wave mixing parametric gain with the near-lowest reported threshold of 16.7 mW for silicon nitride waveguides made with a low temperature process.We report an OPO threshold per unit resonator length of 15.2 mW/mm, lower than reported for low temperature deposited thick waveguides 57 and twice as low as deuterated Si-rich thick nitrides (See Supplementary S11 Table TS7) 60,63 .Significantly, our thin waveguide losses are comparable with that of unannealed LPCVD nitride thin core waveguides of the same geometry (Supplementary Section S9).This dual use capability of our anneal-free process, for both thin and thick core linear and nonlinear devices, with high performance loss, demonstrates the versatility of this platform and application to future heterogeneous and monolithic photonic integration.
We illustrate examples of possible heterogeneous and monolithic integration (Fig. 1) enabled by our anneal-free process.These include deposition of ultra-low loss waveguides on III-V semiconductors (Fig. 1a) for high performance lasers and compound semiconductor photonic integrated circuits 64,65 , preprocessed electronic circuits and silicon photonics 23,36 (Fig. 1b), organic material based integrated circuits 66 for cointegration with silicon nitride PICs and biophotonics 67 (Fig. 1c), thin film lithium niobate 33 (Fig. 1d), and materials like quartz for athermalization of resonators and reference cavities 35 (Fig. 1e).Additionally, this process can be used to realize sophisticated multi-level silicon nitride photonic circuits 68 , homogeneously and monolithically integrated with other materials, to combine high-performance thin-waveguide components like spectrally-pure Brillouin lasers 17 and thick waveguide nonlinear components including optical frequency combs 55,57 (Fig. 1f).

Anneal-Free Fabrication Process and Waveguide Design
In this work we demonstrate that the same process can be used to fabricate oxide clad silicon nitride waveguides that have an order of magnitude variation in nitride core thickness, using the process flow shown in Fig. 2a, realizing the lowest anneal-free silicon nitride waveguide losses to date.This process is used for both thin and thick waveguides, and the wide range of core thickness enables device designs and functions that require different loss regimes and other optical characteristics, such as dispersion, to realize applications as shown in Fig. 2b,c.For example thin ultra-low loss waveguides are required (Fig. 2b) for stimulated Brillouin lasers 17 , spiral resonator optical reference cavities 45 , and grating beam emitters for creating cold atoms 29,69 and thick nitride waveguides (Fig. 2c) are required for OPO and microcombs 56 , supercontinuum generation 55 , and mid-IR photonics and gas sensing 70 .The process independence with respect to waveguide thickness, as well as anneal-free maximum temperatures of 250 °C, demonstrates the potential for co-integration of thin to thick nitride core devices and 3D monolithic and homogeneous integration 14,68 as well as monolithic and heterogeneous integration on a variety of other material platforms.
The anneal-free process (Fig. 2a and described in further detail in the Methods Section) starts with a 1 mm thick silicon wafer substrate with pre-processed 15 um thick thermal oxide lower cladding.A uniform silicon nitride layer (e.g.80 nm or 800 nm) is then deposited using a deuterated silane precursor Inductively Coupled Plasma -Plasma Enhanced Chemical Vapor Deposition (ICP-PECVD) process at 250 °C.The nitride layer is patterned and etched at 50 °C using an Inductively Coupled Plasma Reactive Ion Etcher (ICP-RIE) etch.A final silicon dioxide cladding layer is deposited using the same deuterated silane precursor ICP-PECVD process at 250 °C.In the future, the lower cladding can also be deposited using our 250 °C process for co-integration with other materials and platforms.The different thicknesses of nitride devices correspond to variations in optical mode confinement from dilute modes for thin to strongly confining for thick.The thin waveguide losses are primarily dominated by absorption since nitride sidewall scattering is minimized due to low mode overlap with the core 43 , whereas the thick guide losses are dominated by sidewall scattering 14 .The optical mode for thin nitride waveguides exists predominantly in the oxide cladding, therefore it is essential that the anneal-free fabrication process results in low losses for both the deposited nitride and oxide materials.
Figure 2 Anneal-free silicon nitride photonics integration process, thin and thick waveguides, and applications of each.a Anneal-free fabrication flow.Variation in loss regimes for thin and thick waveguides.b Example applications that require the performance of dilute mode thin nitride waveguides, with absorption dominated losses, include stimulated Brillouin lasers 17 , coil resonator reference cavities 45 , and cold atom trap beam delivery 29,69 .c Examples applications that require the characteristics of strongly confining thick nitride waveguides, with higher scattering dominated losses, include supercontinuum generation, mid-IR photonics and gas sensing 70 , and microcombs and Optical Parametric Oscillators(OPO).
We characterize the composition of our anneal-free deposited nitride using FTIR 47,56 .We use a silicon nitride buscoupled ring resonator configuration to access the anneal-free thin nitride losses and compare it to devices made with an unannealed LPCVD silicon nitride process (see Supplementary section S9).The thin nitride waveguide design is a 6 μm wide, 80 nm thick Si3N4 waveguide core with a 15 μm thick thermal oxide SiO2 lower cladding layer and 5 μm thick oxide upper cladding layer (Fig. 3a) for both the ring and bus waveguides.The ring radius is 8530.8μm for the thin nitride chip as shown in the example reference resonator photograph in Fig. 3b and the ring-bus coupling gap is 3.45 μm as measured with Scanning Electron Microscopy (SEM) prior to upper cladding deposition (Fig. 3c).The thin core waveguide is designed to support one quasi-Transverse Electric (TE) and one quasi-Transverse Magnetic (TM) mode irrespective of process parameter variations (see Supplementary Section S4).The waveguide design used for our anneal-free process is the same as that used in our standard fully annealed LPCVD nitride and TEOS-PECVD SiO2 process 71 .The thick nitride devices have an 800 nm thick nitride core, a 15 μm thick thermal oxide SiO2 lower cladding layer, and a 4 μm thick oxide upper cladding layer (Fig. 3d).Design splits of the thick nitride devices include ring resonators with waveguide widths varying from 1.4 to 2.4 μm for both ring resonator and bus waveguides, ring radii varying from 165 to 177 μm, and ring-bus coupling gaps varying from 200 to 600 nm.Spiral waveguides were also fabricated with lengths of up to 35 cm, with a sample chip shown in the photograph in Fig. 3e.An example topdown SEM image of a ring resonator with a designed 2 μm waveguide width and 300 nm ring-to-bus waveguide gap is shown in Fig. 3f, indicating high quality thick nitride deposition.Cross-sectional SEM images of the thick nitride core are also provided in Supplementary S2 Fig. S1.f Top-down SEM image of a 800 nm thick nitride waveguide ring resonator, with a waveguide width of 1.4 μm and gap of 400 nm on mask.The measured gap is 0.44 μm and measured waveguide widths are 1.32 μm and 1.27 μm respectively.This confirms the high quality of our thick nitride waveguides.

Thin Nitride Loss/Q and Laser Reference Cavity Application
The waveguide losses and resonator Q are measured and calculated for the fundamental TM mode only, using a calibrated Mach Zehnder interferometer (MZI) technique 17,19,43 , and is described in further details in the Methods section.For each thin-nitride resonator design, we characterize 3 different devices (Devices 1-3) and measure TM loss and Q for each device from 1520 to 1630 nm in steps of 10 nm (Fig. 4a).The minimum loss of 1.77 dB/m and maximum intrinsic Q of 14.9 million are measured at 1550 nm.The fabricated devices are over-coupled at wavelengths above 1540 nm, and the maximum Q corresponds to a 4.0 million loaded Q with 49.1 MHz FWHM resonance width (Fig. 4b).The median of the intrinsic Q and loss throughout the above wavelength ranges is 7.77 million and 3.26 dB/m respectively, while the average intrinsic Q and loss are 7.55 million and 4.31 dB/m respectively.Our lowest losses were over half an order of magnitude improvement compared to previous low temperature deuterated devices 57 .
Next, we report on a laser stabilization demonstration using PDH locking of a laser to the resonator device 3 at 1550 nm.The laser frequency noise is measured before and after locking using a calibrated MZI frequency noise discriminator 45 (Fig. 4c).The measurement does not use vibration isolation, acoustic shielding, or temperature control of the resonator reference cavity, hence low frequency noise is dominated by environmental effects.The free-running laser 1/π -integral linewidth 72 is 21.3 kHz and the β -separation linewidth 72 is 195 kHz .After PDH locking to the thin nitride resonator the 1/π -integral linewidth is reduced to 0.976 kHz, a reduction factor of 22, and the β -separation integral linewidth is reduced to 6.94 kHz, a reduction factor of 28.Under PDH locking, the frequency noise is reduced by over 4 orders of magnitude at 0.67 kHz and 1.4 kHz frequency offsets and as low as 20 Hz 2 /Hz at 10 kHz frequency offset from the carrier.Further details of the setup and linewidth calculations can be found in Supplementary Section S8. resonator Pound-Drever-Hall (PDH) locking and frequency noise measurements with an optical frequency discriminator; PD, photodetector; BPD, balanced photodetector; PC, polarization controller; OSC, oscilloscope.d Frequency noise measurements at 1550 nm of the laser free-running vs when PDH locked to the ring resonator cavity.The 1/π -integral linewidth (1/π-ILW) and β -separation linewidth (β-SLW) of the laser reduce by factors of 22 and 28 respectively upon locking.The frequency noise was as low as 20 Hz 2 /Hz at 10 kHz frequency offset from the carrier then.

Thick Nitride Loss/Q and OPO, FWM, and SHG Nonlinear Photonics Applications
Nonlinear photonic waveguides with wavelength-scale core thickness (~1 μm) offer the high optical confinement and waveguide dispersion needed for effective nonlinearities 15,50,52 .Our 800 nm thick devices are fabricated using exactly the same process flow as described above for the thin nitrides, and the waveguide loss and Q measurements are performed as described in the previous section.We demonstrate that these anneal-free 800 nm nitride waveguides and resonators can achieve: 1) Resonant OPO and Kerr-comb formation and 2) non-resonant supercontinuum generation.We simulate and measure the dispersion (see Supplementary S4 Fig. S3, S11 Fig. S13) and the losses of the different geometry variations in our devices, and based on these results set the waveguide geometry to be 2 μm wide with a 300 nm bus to ring coupling gap, and the resonator radius to 175 μm.
The loss and Q values are measured for a wavelength range of 1550 nm to 1630 nm (Fig. 5a).Example calibrated MZI resonance measurements for the lowest losses are shown in Figs.5b,c for the TE and TM modes.These measurements yield losses as low as 8.66 dB/m and 16.4 dB/m and intrinsic Q as high as 4.03 million and 2.19 million, for the TE and TM modes respectively.The loaded Q are measured to be 2.30 million and 1.11 with FWHMs of 82.5 MHz and 172 MHz for the TE and TM modes respectively.The median and average intrinsic Q as well as loss for both polarization modes over the measurement wavelength range given in Table TS3 in Supplementary Section S6.Additional Q measurements for the TE mode around the wavelengths where the Q is maximum confirm that the same data points are not due to measurement error (See Supplementary S10 Fig. S10).In fact, these "outlier" wavelengths occur partially because higher order modes do not interact with the fundamental modes 63 .We further perform measurements for the TE mode on 3 different devices with 165 μm radii with the same waveguide width and gap which confirm that the loss and intrinsic Q measurements are repeatable from device to device (See Supplementary S10 Fig. S11).For nonlinear application of the thick nitride we first demonstrate OPO and Kerr-comb formation in a 175 μm radius microring resonator.The resonator has a cross-sectional waveguide of dimensions 800 x 2000 nm (Fig. 6a,b) and we pump a resonance at 1566.7 nm which has a measured QL ~ 1.6 million and Qi ~ 2.0 million.Figure 6b shows an optical micrograph of one device.Fig. 6c shows OPO at an on-chip pump power of 25 mW.As the pump power is increased, Turing pattern formation modulation-instability comb states 22 are also observed (see supplementary section S11).We measure a threshold power, Pth, for OPO of ~16.7 mW corresponding to an effective nonlinear index, n2 ~ 1.5x10 -19 m 2 /W (see methods section for more details) which is only slightly lower than typical measurements of n2 for stoichiometric nitride devices 73,74 .This corresponds to the lowest threshold power per unit length of 15.2 mW/mm for any low temperature silicon nitride process (See Table TS7 in Supplementary Section S11).
Next we demonstrate broadband supercontinuum generation in 4 mm long, 800 nm thick straight waveguides (Fig. 6d) with widths ranging from 1.6 to 2.4 um.Fig. 6d shows supercontinuum spectra measured by coupling light from a 1550 nm, 100 MHz repetition rate mode-locked laser with 100 fs pulse duration and on-chip pulse energies ~200-400 pJ into the waveguides.The resulting supercontinuum emission covers two octaves, from ~650 nm to ~2.7 µm.CO2 absorption lines in the spectrum analyzer are evident at the long wave side of the spectrum.While the dispersion of these initial devices is not favorable for mid-infrared supercontinuum generation, we have measured absorption spectra of our deuterated nitride (Supplementary Section S2) and oxide layers 48 and, in principle, our films should support waveguiding and supercontinuum generation out to 4 µm.

DISCUSSION
We report the lowest loss waveguides and highest Q integrated ring resonators, 1.77 dB/m loss and 15 million Q, fabricated with an anneal-free silicon nitride photonic low temperature process with maximum processing temperature of 250 °C for all steps.We demonstrate that this anneal free process can be used for both thin and thick nitride waveguides, spanning a 10X thickness range, without requiring stress mitigation techniques or chemical mechanical polishing.Using the exact same process as record-low loss thin nitride waveguides, we achieve 8.66 dB/m loss and 4.03 million Q for 800 nm thick nitride waveguides, the highest reported Q for a low temperature processed resonator with equivalent device area (See Supplementary Section S6).We report both linear and nonlinear applications using thin and thick core resonators, demonstrating record performance for both types of applications and an anneal-free fabrication process.Laser noise reduction is demonstrated by PDH locking a laser to an ultra-low loss 80 nm thin nitride resonator employed as an optical reference cavity, achieving 4 orders of magnitude reduction in laser frequency noise.This was possible due to the more than order of magnitude larger modal area of thin nitrides compared to the thick and the long resonator length resulting in a TRN floor which was 10 3 times smaller than a typical thick nitride resonator (See Supplementary Section S8).A high-Q 800 nm thick nitride resonator is used to achieve resonant OPO with a 16.7 mW threshold corresponding to an OPO threshold per unit resonator length of 15.2 mW/mm and Kerrcomb formation, and over 2 octave non-resonant supercontinuum generation.The low 250 °C temperature and uniformity of this process across waveguide thickness and design, will enable a wide range of systems on-chip applications and novel integration approaches including direct processing on organics, circuit cards, silicon photonic and III-V compound semiconductors, lithium niobate, as well as enabling 3D integration stacking geometries that combine circuits with different nitride core thickness 14,68 .The thin and thick nitride devices cover two different loss regimes, the thin dominated by absorption loss of the cladding material, and the thick by scattering loss and core absorption (Fig. 2b,c).We confirm this for our thin nitride devices at 1550 nm by measuring the thermal bistability for different on-chip powers giving us an absorption loss fraction of 59 % corresponding to an absorption limited loss of 1 dB/m (Supplementary section S7), comparable with 90 nm annealed LPCVD nitride cores with a deuterated oxide cladding 48 .Previously reported work on thick core low temperature nitrides using deuterated processes 55,57,60 as well as sputtering 61 did not demonstrate low absorption loss for their upper claddings and hence ultra-low loss thin nitride devices were not achieved.The absorption losses in our thin nitride devices are thought to be partially from the unannealed thermal oxide lower cladding, which can be further improved by depositing deuterated SiO2 for the lower cladding, a subject of future work.The small amount of hydrogen present in the deuterated silane precursor also increases the absorption loss as evidenced by the increase in waveguide loss towards 1520 nm (Fig. 4a) which is near the 1st overtone of the SiN-H bond absorption.Towards 1630 nm, the loss increase is most likely due to overtones of the SiO-D bond in the upper cladding 48 .We additionally see that the thin losses are comparable to devices of the same geometry made with unannealed LPCVD nitride (Supplementary section S9) confirming that our losses are competitive with respect to process temperature.The more tightly confined modes in the 800 nm thick devices have higher sidewall scattering losses than their thin nitride counterparts, and could be improved by using a hard mask with a smaller grain size such as those made with Atomic Layer Deposition 75,76 or RF sputtering 77 .The TM mode loss for the thick nitride is very different compared to the loss for the TE mode, as the top surface roughness of the nitride core is much lower than the etched sidewall roughness, and the two modes are significantly different in shape (See Supplementary Section S4).It should also be noted that our highest intrinsic Q thick nitride resonances exhibit resonance splitting (see Supplementary Section S6) which is believed to be due to the scattering loss fraction being higher at those resonance wavelengths 43 .In this process we utilized ICP-PECVD with deuterated silane and nitrogen precursors for silicon nitride deposition, avoiding ammonia due to the concentrated Inductively Coupled Plasma (ICP) induced dissociation of N2 that cannot be achieved with conventional parallel plate PECVD 78 , and eliminated hydrogen absorption losses 47,55,57,60 .Alternative low temperature processes to ours include sputtering and conventional Plasma Enhanced Chemical Vapor Deposition (PECVD) 79,80 but both suffer from high particle count related scattering losses and conventional PECVD-grown silicon nitride suffers from high hydrogen related absorption losses due to using ammonia and silane precursors 80,81 .Both the linear and nonlinear refractive indices (see Supplementary section S3) are close to that measured for stoichiometric silicon nitride 80 .A summary of published losses and intrinsic Q near the C-band of ring resonators made with different processes as a function of maximum processing temperature and their nitride processing methods is given in Fig. 7, and compared to this work.Our reported lowest losses fall in an "optimum" region between loss and process temperature.It should be noted also that the record low loss thick nitride devices had a width of 10 µm 52 .Our anneal-free process, with a maximum processing temperature of 250 °C, and uniformity for core thickness spanning an order of magnitude, is fully CMOS-compatible and will pave the way to monolithic and heterogeneous integration of ultra-low loss silicon nitride photonics with material systems not possible before such as III-V semiconductors 31,37 , lithium niobate 33 , preprocessed silicon circuits and photonics 40 , and organic electronic materials 39 , with applications in metrology 9 , navigation 8 , telecommunications 10 , and quantum information sciences [2][3][4] , and consumer electronics where organic electronics is widely used 82 .This process could also be used to monolithically and homogeneously integrate both thin low confinement and thick high confinement silicon nitride waveguides, enabling 3D integration with optimized device footprint and linear and nonlinear performance.In the future, the temperature of our process has the potential to be modified for as low as 50 °C using further process development on our ICP-PECVD tool 83 (which supports 50 °C processes), enabling the monolithic integration of ultra-low loss photonic integrated circuits on most organic electronic materials.Our lowest losses (thin nitride) are near an "optimum", denoted by the oval, between low loss and temperature, the current record low loss also being a thin nitride device.Our thick nitride structures have double the Q of the current record calculated for low temperature fabricated devices with similar areas 57 as marked with the C, and very similar loss overall to the absolute record, while having an area 7.5 times smaller.The different works compared include Inductively Coupled Plasma-Plasma Enhanced Chemical Vapor Deposition (ICP-PECVD) processes using deuterated silane precursors like (I) This work, (II) Y. Xie et al. 45 , (III) J. Chiles et al. 55 , and (IV) X.X.Chia et al. 60 -which also uses Si-rich SiN ; Sputtering such as (V) A. Frigg et al. 79 , (VI) S. Zhang et al. 61 ; Plasma Enhanced Chemical Vapor Deposition (PECVD) in conjunction with Chemical-Mechanical Polishing(CMP) (VII) X. Ji et al. 84 ; Pulsed Laser Deposition -(VIII) N. Golshani et al. 85 ; And Low Pressure Chemical Vapor Deposition (LPCVD) together with annealing, such as (IX) Z. Ye et al. 86 , (X) X. Ji et al. 52 , (XI) K. Liu et al. 42 , and (XII) J. Liu et al. 87 -which uses a Damascene process too.

METHODS Fabrication Process
The thick and thin SiN core, and SiO2 upper cladding depositions are performed using an Unaxis VLR ICP-PECVD tool with the same processes used for all core thicknesses and devices.Further details on the nitride deposition and oxide deposition processes can be found in Supplementary section S1.Before any deposition on a device wafer, we run a deposition on a test 100 mm silicon wafer and measure the particle counts, as well as the film thickness and refractive index with an ellipsometer.The deposition on the device wafer is performed only if the particle counts increase by less than 300.The fabrication starts with the 250 °C silicon nitride deposition on Si wafers with 15 μm of thermal oxide, with the thick nitride depositions merely being done for longer than the thin nitride deposition, in a single step.After the nitride deposition step, the thick nitride wafers only get 40 nm of Ruthenium DC sputtered.Both the thick and thin nitride wafers are then patterned in a 248 nm DUV stepper, using the same lithography parameters.The thin nitride is then etched in an ICP-RIE using a CF4/CHF3/O2 chemistry, after which it is ashed in a O2 plasma in a ICP tool to remove etch byproducts.Any remaining photoresist is stripped by sonicating in a hot N-methyl-2pyrrolidone (NMP) solution and rinsing in isopropanol.We additionally perform a standard piranha clean at 100 °C followed by a base piranha (5:1:2 solution of H2O:NH4OH:H2O2) clean at 70 °C , both in freshly prepared solutions, making the thin nitride wafers ready for upper cladding deposition.For the thick nitride fabrication, the Ru on the thick nitride is etched in an ICP-RIE too, to create a hard mask, using a Cl2/O2 chemistry.The thick nitride wafer is then stripped of photoresist the same way as the thin one, using hot NMP solution and isopropanol.It is then etched in an ICP-RIE using CF4 only, after which the same O2 plasma ashing as the thin nitrides is done.Any remaining Ru is stripped in a wet etch, and then the same piranha cleans done for the thin nitrides are performed.The requisite amount of ICP-PECVD SiO2 upper cladding is then deposited at 250 °C on both the thin and thick nitride wafers.The flow diagrams of these fabrication processes can be found in Supplementary Section S5.

Quality factor measurements and calculation
The loaded quality factors of the ring resonators are measured using three different calibrated unbalanced fiber MZIs with MZI fringe widths of 5.87 MHz, 18 MHz, and 200 MHz.We have seen in our previous works that Q values measured with this method match well with cavity ring-down measurements 88 .Two Newport Velocity TLB-6700 tunable lasers are used, one with a tuning range of 1520 to 1570 nm, and another one with a tuning range from 1550 to 1630 nm.These lasers are tuned in wavelength with piezo actuators, by applying a ramp signal to the same.A polarization controller is present before the input to the thin nitride devices, which is edge-coupled to a single mode cleaved fiber, while there is a polarization beam splitter present before the input to the thick nitride devices.The full setup for the thin nitride measurements is shown in Supplementary section S6 Fig. S6.Loaded and intrinsic quality factors are extracted by fitting the resonance transmission to a Lorentzian (thin nitride) or coupled-Lorentzian (thick nitride) curves.Coupling and loss parameters are determined by measuring the ring-to-bus couplings on independent ring-bus coupling structures as well as simulating the same 35 .Additional details can be found in supplementary section S6, and plots of all resonance measurements in the Supplementary : Resonance Measurement Summary file.

Threshold power for optical parametric oscillation
We determine the effective nonlinear index for our deuterated nitride by measuring the threshold power for OPO, Pth, according to the following 15 : where n is the effective refractive index, Aeff is the effective mode area, νFSR = 133.5 GHz is the resonator free spectral range, vo is the pump frequency, Qi is the resonator intrinsic Q, and K is a resonator coupling constant K = Qi/Qc, where Qc is the resonator coupling Q.We extract values of Qi and Qc through the Lorentzian curve fitting method described above.We then use the software Lumerical MODE to calculate Aeff and n as a function of wavelength (in this case 1.35 µm 2 and 1.85 respectively).Based on our analysis, we determine n2 ~ 1.5 ± 0.2x10 -19 m 2 /W.Measurement uncertainty is propagated from measurement resolution of the threshold power and the one standard deviation error of the curve fitting parameters which determine Q values.Using index data for our nitride and oxide films measured via ellipsometry, Lumerical MODE solver was used to calculate dispersion curves for our 800 nm thick waveguides for a range of widths from 1.5 μm to 2.5 μm, in steps of 0.5 μm for 800 nm of nitride.Figure S3 shows dispersion data for our thick nitride structures which exhibit anomalous dispersion near 1550 nm (red dashed line).where QLoad is the loaded quality factor.  is the group index of the waveguide,  = 2R is the perimeter of the ring resonator, res is the resonant wavelength,  = √1 −  2 is the self-coupling coefficient and  2 is the power coupling coefficient, a is the single-pass amplitude transmission and is related to the power attenuation coefficient  as  2 = (-).The intrinsic Q of the resonator can be calculated with the extraction of waveguide propagation loss  using the following equation 7 .

(ES4)
The group indexes we use for equation ES4 for loss calculations are from Free Spectral Range (FSR) measurements and are 1.4642 for the 80 nm x 6 μm thin nitride TM mode 8 , and 2.025 and 2.053 in the TE and TM modes for the 2 μm wide 800 nm thick devices.
For the ICP-PECVD thin nitride resonators, the TM resonances for all devices below 1550 nm are undercoupled, while almost all resonances 1550 nm and above are overcoupled.As an example to determine whether a TM mode is under or overcoupled, we take the case of our lowest loss 1.77 dB/m resonance at 1550 nm.The simulated ring-bus field coupling (k) using refractive indices from ellipsometry at 1550 nm (Table TS1) and the actual waveguide dimensions (Fig. 3c) using Lumerical FDTD is 0.2141.The undercoupled solution for this resonance gives a k of 0.14, while the overcoupled solution gives a k of 0.2379 which is within the tolerance of our measurement to the simulated value.The overcoupled value of k here also agrees better with measurements of k from ring-bus coupling structures present on the same chip (Fig. 2b).The TE mode resonances for the thin nitrides are all undercoupled, and are difficult to measure accurately to calculate Qi and loss for all wavelengths for all of the devices because of the low extinction of the resonances.For the unannealed Low Pressure Chemical Vapor Deposited (LPCVD) devices in Section S7, the TM modes are all overcoupled.
The resonances for the thick nitride resonators shown are all undercoupled for both the TE and TM modes.These resonances are fit to a modified lorentzian curve to account for resonance splitting caused by backscattering in the ring 9 .Some statistics about the Qs and losses measured of the 2 μm waveguide width and 300 nm gap thick nitride device is given in Table TS3 below.The loss and Q of the low temperature thick nitride devices with similar area were calculated using the same split resonance model as we used for our own devices and fitting to the data in the "Fig.3c" in Y. Xie et al 10 .This resonance had a loaded Q of 1.5 million, at 1560.39 nm, with a Free Spectral Range (FSR) of 150 GHz as given in Y. Xie et al 10 , yielding an intrinsic Q of 2.9 million and loss of 11.9 dB/m.

S7. Absorption loss estimation
We measure the absorption loss at 1550 nm of thin nitride device 3 to separate the contributions of absorption and scattering losses to the total loss.This measurement follows a technique to quantify the photothermal induced bistable linewidth shift of the longitudinal ring resonances 9 , using a spectral scan across the resonance with a high on-chip power, to induce a photothermal resonance redshift that is comparable to the resonance linewidth.This photothermal effect is due to absorption heating in the resonator.As shown in Fig. S7a, the red detuning (from shorter to longer wavelengths) across resonance heats up the resonator, and induces a resonance redshift, resulting in a skewed lineshape.To extract the absorption loss relative to the total loss, we simulate the thermal impedance Rth of the ring resonator in Comsol®, giving us Rth = 6.87 K/W.We then measure the thermal-optic redshift with a global heating Δfres/ΔT = 1.23 GHz/K which yields the resonance redshift per milliwatt of optical power absorbed by the resonator Δfres/Pabs = 8.45 MHz/mW.The resonance redshift has a linear relationship with on-chip power (Fig S8b ), confirming the photothermal heating effect, from which we extract the absorption loss fraction to be 59 %.This yields an absorption loss of 1.04 dB/m, which can be said to be an upper bound for the absorption loss of the cladding in this device.Some of this absorption loss might come from the 1520 nm loss peak (See W.Jin et al 1 and our(Fig.4a)) due to SiN-H bonds in the nitride due to residual hydrogen, even for thin nitrides.

S8. Thermorefractive Noise (TRN) Floor Estimation, PDH locking and frequency noise measurements
From the modal area (Table TS3) and cavity length of a device, one can estimate the thermorefractive noise (TRN) floor of said cavity 11 .Our thin nitride cavity is hence estimated to have a TRN floor of around 10 Hz 2 /Hz which is more than 3 orders of magnitude lower than the TRN floor for a typical thick nitride ring resonator enabling us to lower the frequency noise of a locked laser to a cavity by 3 orders of magnitude more than would be possible with a typical thick nitride device.In the case where one makes a thick nitride resonator with as long a length as the thin nitride mode size is larger (27 times), one will still not be able to reach as low frequency noise when locked as the same also depends inversely on the quality factor 11 .Further, increasing a thick nitride resonator length to 1.5 m would increase the waveguide loss typically due to increase in the total number of accumulated defects in the resonator waveguide, further increasing the lowest frequency noise possible.
Laser frequency stabilization was achieved using a standard Pound Drever Hall locking arrangement, as shown in Fig. 4c, and described in detail in K. Liu et al 11 .A velocity TLB 6730-P tunable External Cavity Diode Laser (ECDL) was used as the laser source, with 30 MHz phase modulated sidebands applied via current modulation.Approximately 1 mW optical power was delivered to the resonator, and the resulting transmission signal was photodetected with a 10 kV/A Trans-Inductance Amplifier (TIA) amplified photodetector.Frequency noise measurements were carried out using an unbalanced Mach-Zender interferometer with a 200m delay length as in Fig. S8, and described in detail in G. Brodnik et al 12 .
The low frequency cutoff for the linewidth calculation was 300 Hz, and the high frequency cutoff was 990,000 Hz.

S9. Thin nitride loss comparison with LPCVD nitride
We compare the losses of devices made using the thin nitride geometry (80 nm x 6 μm) between those using deuterated ICP-PECVD nitride cores to those using unannealed Low Pressure Chemical Vapor Deposited (LPCVD) cores, both using the same deuterated upper cladding, for a fair comparison.We see that at 1550 nm and above, the losses are very much comparable.

S10. Additional Q/loss measurements of thick nitride devices
Additional Q measurements of the thick nitride TE modes for the 175 μm radius device around the wavelengths where the loss minima or outliers in wavelength occur in Fig. 5a are taken (Fig. S10) namely around 1580, 1600, and 1606 nm respectively, showing that these are not measurement discrepancies and may be related to avoided mode crossings with higher order modes.We also take more Q/loss measurements of 3 different ring resonator devices with 165 μm radii, but also having a 300 nm ring-bus gap and 2 μm wide waveguide as for the devices in Fig. 5, for the TE modes.The losses and Qs being fairly consistent across the different devices shows that our process is reliable (Fig. S11).

S11. Calculations and additional non-linear application measurements of thick nitride devices
The Optical Parametric Oscillation (OPO) thresholds and thresholds per unit length of various works are calculated and shown below in Table TS4.Kerr comb formation was measured using a widely tunable ECDL amplified by a high power EDFA.The laser frequency was tuned to be slightly blue detuned from a TE mode resonance located at 1566.7 nm (at low optical power), and the resonator output was monitored with an optical spectrum analyzer.As optical power was increased, the laser frequency was slowly tuned to maintain the smallest possible blue detuning between laser and resonator.Onchip power was calculated by subtracting half the total throughput coupling loss of the resonator from the measured input optical power to the chip.At on-chip powers higher than 40 mW, The comb transitions into the modulation instability regime, as seen in Figure S12 below.Due to difficulties with strong thermal shifting and a large number of avoided mode crossings, soliton steps were not able to be observed.To confirm that the device is able to support soliton formation, a temporal lugiato-lefever equation simulation 16 was used to simulate soliton formation dynamics of the 2000 nm TE mode ring-resonator, using dispersion information measured(Fig.S13 (b)) via a widely tunable continuous laser sweep.Figure S13 (a) below shows a laser detuning sweep with 600 mW on-chip power that results in multiple soliton steps.

Figure 1
Figure 1 Examples of different applications of the anneal-free silicon nitride process.: Cointegration with a Compound semiconductors for high performance lasers, b preprocessed silicon circuits and silicon photonics, c organic electronics/photonics, and d thin film lithium niobate.e Thermal and substrate engineering such as with quartz substrates.f Homogenous integration of thick ( > 650 nm) and thin nitride core devices, each used for different applications.

Figure 3
Figure 3 Material and device characterization and geometries for thin and thick nitride anneal-free devices.a Thin nitride waveguide geometry.b Thin nitride chip showing ring resonators, ring-bus coupling and other test structures.c Top-down Scanning Electron Microscopy (SEM) image of the thin nitride waveguide with a width of 6 μm and gap of 3.5 μm on mask.Measured gap is 3.44 μm, and waveguide widths 6.01 and 5.96 μm respectively.d Thick nitride waveguide geometry.e A thick nitride chip showing a bend loss spiral, ring-bus coupling and other test

Figure 4
Figure 4 Thin nitride Q and loss measurements.a The loss and intrinsic Q variation of the Transverse Magnetic (TM) mode vs wavelength for 3 different devices.b Q measurement of the TM mode resonance in device 3 at 1550 nm that yields the lowest loss and highest Q of 1.77 dB/m and 14.9 million respectively.The loaded Q and Full Width Max (FWHM) are 4.0 million and 49.1 MHz respectively.c The setup for the laser to

Figure 5
Figure 5 Thick nitride Q and loss measurements.a Loss and intrinsic Q variation vs wavelength for the Transverse Electric (TE) and Transverse Magnetic (TM ) modes from 1550 to 1630 nm wavelengths.b The TE mode resonance Q measurement at 1581 nm yielded the lowest loss of 8.66 dB/m and highest intrinsic Q of 4.03 million.The loaded Q and Full Width Max (FWHM) are 2.3 million and 49.1 MHz respectively.c The lowest loss TM mode resonance Q measurement at 1560 nm.All measurements shown here are for 175 μm radius ring resonators with 2 μm wide waveguides.

Figure 6
Figure 6 Nonlinear application demonstrations for anneal-free thick 800 nm waveguides and resonators.a Large field of view image of a thick nitride chip with a broad scan of ring resonator designs and straight waveguides.The green and blue highlighted regions correspond to devices tested in (c) and (d) .b Dark-field optical micrograph of the ring resonator device used for Kerr-comb measurement.c Optical spectrum of the ring resonator output showing the onset of optical parametric oscillation.d Broadband supercontinuum spectra from the different width waveguides highlighted in light blue in (a).

Figure 7 Q
Figure 7 Q and loss vs temperature near the C-band for different published works based on their silicon nitride growth methods and processing compared to this work.Our lowest losses (thin nitride) are near an "optimum", denoted by the oval, between low loss and temperature, the current record low loss also being a thin nitride device.Our thick nitride structures have double the Q of the current record calculated for low temperature fabricated devices with similar areas57 as marked with the C, and very similar loss overall to the absolute record, while having an area 7.5 times smaller.The different works compared include Inductively Coupled Plasma-Plasma Enhanced Chemical Vapor Deposition (ICP-PECVD) processes using deuterated silane precursors like (I) This work, (II) Y. Xie et al.45 , (III) J. Chiles et al.55 , and (IV) X.X.Chia et al.60 -which also

Figure
Figure S2 below shows mode simulations for the TM mode for the 80 nm x 6 μm thin and both TE and TM modes for the 800 nm x 2 μm thick nitride core devices respectively, from Lumerical MODE solver.

Figure S2 Mode simulations. for a 80 nm
Figure S2 Mode simulations.for a 80 nm Transverse electric (TE) Mode b 80 nm Transverse magnetic (TM) Mode c 800 nm TE Mode d 800 nm TM Mode.The 800 nm nitrideBelow are the effective areas of different modes for the thin and thick nitrides.The order of magnitude larger modal volume of the thin nitride mode makes it ideal for use as a reference cavity, while the smaller thick nitride modes are better for exploiting the Kerr effect.

Figure S3
Figure S3 Waveguide dispersion simulations for different waveguide widths

Figure
Figure S4 Detailed fabrication process flow for thin nitride devices.PR = Photoresist, BARC = Bottom anti-reflective coating.

Figure
Figure S5 below shows our complete fabrication process flow for the thick nitrides.

Figure S5
Figure S5 Detailed fabrication process flow for thick nitride devicesS6.Quality factor measurement and loss extraction/calculationThe calibrated Q setup used to measure the Quality factors and loss for the thin nitrides is given Fig.S6below.The setup for the thick nitrides is exactly the same, except it uses a polarization beam splitter before the Device-Under-Test (DUT).

Figure S6
Figure S6 Calibrated unbalanced Mach-Zehnder Interferometer (MZI) setup for Q factor measurementsThe full-width-at-half-maximum resonance width of the single bus ring resonators is measured with the radio frequency calibrated Mach-Zehnder interferometer (MZI) to extract the quality factor.The propagation loss of the waveguide is extracted based on the following equation 6 ,

Figure S7 .
Figure S7.Photo-thermal heating and absorption loss measurement.a Photothermal effect is amplified by higher on-chip power and the resonance redshift exhibits a linear relationship with the on-chip power.b Normal Lorentzian fitting for the lower power spectral sweeping and skewed Lorentzian fitting for the high power spectral sweeping extracts the intrinsic loss and absorption loss rates.

Figure S8
Figure S8 Detailed system diagram for laser frequency noise measurement using an optical frequency discriminator.

Figure
Figure S9 Loss comparison between thin nitride devices made using different processes.The losses of our 250 °C Inductively Coupled Plasma-Plasma Enhanced Chemical Vapor Deposition (ICP-PECVD) process devices are similar to those made using unannealed Low Pressure Chemical Vapor Deposition (LPCVD) nitride cores, both using the same deuterated upper cladding.

Figure
Figure S10 Additional Q/loss measurements near loss minima.Additional Q/loss measurements were taken around 1580, 1600, and 1606 nm respectively showing consistency of the Q/loss values between measurements.

Figure S11
Figure S11 Loss and Q comparison between 3 different thick nitride ring resonator devices of radius 165 um, 2 um wide waveguide, with 300 nm ring-bus gaps for the TE modes.Our loss and intrinsic Qs are fairly consistent across the different devicesThe median and average losses for TE modes for these devices is given in TableTS5below.Table TS6.Median and average intrinsic Q and losses for the three 165 μm ring resonator devices

Figure
Figure S12 Kerr comb formation.Thick nitride Kerr comb evolution at various on-chip pump powers.

Figure S13 ( a )
Figure S13 (a) Simulated Intra-cavity power versus laser-resonator detuning at 600 mW pump power on chip.Multiple step-like transitions demonstrate the existence of multiple soliton states at high pump powers.(b) Integrated dispersion for the TE mode of the 2000 nm thick resonator, showing significant variance in FSR, as well as some strong avoided mode crossings.